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Molecular Structure, Electronic Structure and Heats of Formation of Explosive Sensitizers
ACTA PHYSICO-CHIMICA SINICA Volume 23, Issue 2, February 2007 Online English edition of the Chinese language journal Cite this article as: Acta Phys. -Chim. Sin., 2007, 23(2), 192-197.
ARTICLE
Molecular Structure, Electronic Structure and Heats of Formation of Explosive Sensitizers Xiulin Zeng*,
Wanghua Chen,
Jiacong Liu
School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Abstract:
Quantum chemical calculations at the HF/6-31G* and B3LYP/6-31G* levels have been carried out on five explosive
sensitizers: ethyl nitrate (EN), n-propyl nitrate (NPN), isopropyl nitrate (IPN), 2-ethylhexyl nitrate (EHN), and tetraethylene glycol dinitrate (TEGDN). Theoretical studies have yielded a wealth of quantum chemical information on the molecular geometries, electronic structures, and energies of the title compounds. On the basis of the Mulliken populations and bond lengths, the O2−N3 fission is acceptable. Charge distribution analysis indicates that the five nitrates produce NO2 gas during the dissociation of the O2−N3 weak bond. The relative thermal stability ordering of the five nitrates was estimated on the basis of the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE). The heats of formation (HOFs) of the five sensitizers, EN, IPN, NPN, EHN, and TEGDN, were calculated from the isodesmic reactions and were −155.972, −190.896, −175.279, −272.376, and −790.733 kJ·mol–1, respectively. Key Words:
Explosive sensitizers; Mulliken population; Frontier orbital energy; Heat of formation (HOF); Isodesmic reaction
The major challenge in the design and application of explosives is the achievement of the right oxygen and fuel mixture to ensure the development of high overpressure and high temperature. In military explosives, some sensitizers are commonly added to the mixture, making it more easy for the mixture to be ignited and to grow to detonation from hot spots such as those caused by sparks, flame, and other sources of heat and high temperature. These sensitizers are relatively unstable molecules, and their decomposition at low temperatures produces free radicals[1−7]. Heat of formation (HOF) is the key property that is used to assess the potential performance of an energetic material in a gun or warhead. Also, HOF is an importance aspect of research in thermochemistry and is directly related to the output properties of an explosive. Using the HOFs of detonation products and explosives, detonation parameters such as heat of detonation, temperature of detonation, detonation velocity, and CJ pressure of detonation[8−14] can be predicted. The sensitizers investigated in this study are ethyl nitrate (EN), n-propyl nitrate (NPN), isopropyl nitrate (IPN), 2-ethylhexyl nitrate (EHN), and tetraethylene glycol dinitrate (TEGDN).
Organic nitrates have been known since the early 1900s. The chemistry of organic nitrates has been a significant area of research since 1930s. Comprehensive reviews are available on their use as additives to explosives and propellants. Since then, organic nitrates have been extensively investigated for their potential use as reactive species in other areas of science and technology. Organic nitrates have also been used to improve ignition in automotive fuels[15−27]. The five acyclic nitrates investigated in this study are used as explosive sensitizers because they possess a weak O−N bond, which is the site of thermal and chemical reactivity. Despite the growing interest in the development of explosives, relatively few quantum chemical computations on explosive sensitizers have been reported so far. Geometrical information is important for understanding the molecular properties of sensitizers that contribute to the sensitizing mechanism; therefore, theoretical calculations have been performed using ab initio and density functional methods. There are several methods that can be used to predict the heats of formation of gas phases from quantum mechanical calculations. Although HOFs were not calculated directly using the
Received: June 21, 2006; Revised: September 14, 2006. * Corresponding author. Email: [email protected]; Tel: +8625-84315526-808. Copyright © 2007, Chinese Chemical Society and College of Chemistry and Molecular Engineering, Peking University. Published by Elsevier BV. All rights reserved. Chinese edition available online at www.whxb.pku.edu.cn
Xiulin Zeng et al. / Acta Physico-Chimica Sinica, 2007, 23(2): 192-197
ab initio MO method and the density functional theory (DFT) method, the results of the geometries and the energies obtained using the two methods are quite reliable. Therefore, the isodesmic reaction has to be designed to derive the HOFs from the calculated total energies and the vibrational analysis results[28−38]. In this study, theoretical calculations were carried out on five explosive sensitizers at the HF[39] and B3LYP[40,41] levels, using the 6-31G* basis set[42]. The molecular geometries, the electronic structure, and the frontier orbital energy were obtained and the HOFs were evaluated.
ΔnRT for the reactions of an ideal gas. For the isodesmic reactions (1a) and (1b), Δn=0, and hence Δ(pV)=0. Computations have been carried out using the Gaussian 98 package[47] at the B3LYP and HF levels on a Pentium personal computer in Safety Engineering and Technology Laboratory. The optimizations were carried out without any symmetry restrictions using the default convergence criteria in the programs. All the optimized structures were characterized as true local energy minima on the potential energy surfaces without imaginary frequencies.
1
2
Computational methodology
The full geometry optimizations of the five sensitizers, EN, NPN, IPN, EHN, and TEGDN, were carried out using Becke′s three-parameter hybrid method and the exchange functional of Yee, Yang, and Parr[40], with the 6-31G* basis set. These computations were also done at the HF level with the 6-31G* basis set. The molecular structure and other parameters were obtained. Isodesmic reactions were designed to predict the HOFs of the five title compounds. Errors in the absolute quantities from quantum chemical calculations are often systematic. To compensate for some of the systematic errors, isodesmic reactions, which conserve the number of each type of bond in the reactants and products, are used to obtain more accurate heats of formation. The so-called isodesmic reaction processes, in which the number of each kind of formal bond is conserved, are used with the application of the bond separation reaction (BSR) criteria[43,44]. The HOFs of the five sensitizers at 298 K were calculated from the following isodesmic reactions: CnH2n+1ONO2+(n−1)CH4→(n−1)C2H6+CH3ONO2 (1a) O2NO(CH2CH2O)4NO2+2CH4+3H2O→ 2HOCH2CH2OH+2CH3CH2OH+2CH3ONO2 (1b) where n is the number of carbon atoms in the title compound. Eq.(1a) is treated as an isodesmic reaction for EN, IPN, NPN, or EHN, and Eq.(1b) is treated as an isodesmic reaction for TEGDN. For reactions (1a) and (1b), the heat of the reaction ΔH298 at 298 K can be calculated from the following equation: ΔH298=ΣΔHf,P−ΣΔHf,R (2) where ΔHf,R and ΔHf,P are the HOFs of the reactants and products at 298 K, respectively. Both the experimental HOFs of the reference compounds CH4, C2H6, CH3ONO2, H2O, C2H5OH, and HOCH2CH2OH are available from Refs.[45,46]. The HOFs of the five title compounds can be determined when the heat of the reaction ΔH298 is known. ΔH298 can be calculated using the following expression: ΔH298=ΔE298+Δ(pV)=ΔE0+ΔZPE+ΔHT+ΔnRT (3) where ΔE0 is the change in the total energy between the products and the reactants at 0 K, ΔZPE is the difference between the zero-point energies (ZPE) of the products and the reactants at 0 K, and ΔHT is the thermal correction from 0 K to 298 K. The Δ(pV) value in Eq.(3) is the pV work term; it is equal to
Results and discussion
2.1 Molecular structure The optimized geometries of the five acyclic nitrates and the atom numbering are shown in Fig.1. The geometrical parameters are first discussed. There is a noticeable feature in the optimized geometry of TEGDN. The following discussion only deals with its half moiety because of the completely symmetrical geometry of TEGDN. The selected bond lengths, the bond angles, and the dihedral angles at the HF/6-31G* and B3LYP/6-31G* levels for the title compounds are shown in Table 1. As seen from Table 1, the calculated structural parameters at the HF/6-31G* level are consistent with those at the B3LYP/6-31G* level. For the bond length of C1−O2, O2−N3, N3−O4, N3−O5, and C1−C6, the HF values are shorter compared with B3LYP results, and for the bond angle of C1−O2−N3, O2−N3−O4, and O2−N3−O5, the HF values are larger than the B3LYP results. In addition, when compared with the experimental geometrical parameters[48−51], the results obtained at the B3LYP level are more favorable than those obtained at the HF level because the former method fully takes into consideration the effects of electron correlation and repulsion.
Fig.1
The structures and atom numbering of the five sensitizers
Xiulin Zeng et al. / Acta Physico-Chimica Sinica, 2007, 23(2): 192-197
Table 1 Compound EN
NPN IPN EHN TEGDN
The selected geometrical parameters of the five sensitizers at the HF/6-31G* and B3LYP /6-31G* levels
Method HF/6-31G* B3LYP/6-31G* Exp. HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G*
C1−O2 0.1441 0.1452 0.1443 0.1438 0.1449 0.1454 0.1466 0.1442 0.1452 0.1433 0.1443
Bond length (nm) O2−N3 N3−O4 N3−O5 0.1329 0.1177 0.1188 0.1415 0.1207 0.1216 0.1405 0.1204 0.1209 0.1328 0.1178 0.1187 0.1412 0.1208 0.1216 0.1328 0.1178 0.1188 0.1410 0.1208 0.1217 0.1329 0.1178 0.1188 0.1416 0.1207 0.1215 0.1330 0.1177 0.1186 0.1416 0.1206 0.1214
C1−C6 0.1515 0.1520 0.1519 0.1517 0.1523 0.1518 0.1524 0.1527 0.1533 0.1516 0.1524
C1O2N3 117.4 114.6 113.0 116.4 114.1 118.0 115.6 117.4 114.7 116.3 113.8
Bond angle and dihedral angle (degree) O2N3O4 O2N3O5 C1O2N3O4 C1O2N3O5 114.2 118.4 −177.8 2.5 2.9 112.5 118.0 −177.5 112.2 118.2 0.0 114.0 118.1 −180.0 0.0 112.8 117.6 −180.0 −2.9 113.8 118.6 177.5 −2.5 112.6 118.3 178.0 3.1 113.8 118.5 −177.3 3.3 112.5 118.1 −177.2 0.0 113.9 117.9 −180.0 0.0 112.6 117.4 −180.0
See Fig.1 for atom numbering; experimental results of EN from Ref.[48−51].
Previous experimental and theoretical studies[25−27,48] have shown that the CO−NO2 group in nitric esters normally has a planar framework. From Fig.1 and Table 1, it can be seen that the C−O−NO2 of the two linear nitrates, NPN and TEGDN, are completely coplanar. The C−O−NO2 of the two-branched nitrates, IPN, EHN, and EN, are essentially planar. These results imply that rotation around the O−N in the nitrates is hardly possible. However, it should be mentioned that there is a noticeable variation in the values of the C1−O2 and O2−N3 bond lengths compared with the other parameters, implying that these geometrical parameters are more sensitive to different molecular structures. Moreover, by comparing the bond lengths among O2−N3, N3−O4, and N3−O5, it was found that the bond length of O2−N3 was obviously larger than that of the other two. It is well known that the shorter the bond length, the stronger the strength of the bond and vice versa. Hence, it can be concluded that the dissociation of the O2−N3 bond is the most probable pathway for acyclic nitrates in the gas phase. 2.2 Electronic structure Table 2 shows the selected atomic charge distributions and the dipole moments μ of the five sensitizers obtained at the HF/6-31G* and B3LYP/6-31G* levels. The charge on the α-C(C1) atoms obtained using the two methods are all negative and very similar in value in EN, NPN, EHN, and TEGDN, but the charge on the α-C(C1) atom in IPN was positive because of Table 2 Compound EN NPN IPN EHN TEGDN
Method HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G*
−CH3 substitution to the α-carbon. This is an expected result because the α-C(C1) atoms of EN, NPN, EHN, and TEGDN are secondary C atoms and that of IPN is a tertiary C atom. It is interesting to note that the atomic charge in the O−NO2 groups is almost identical in the case of the five title compounds. The relatively higher positive charge on the N3 atoms and the negative charge on the O4 and O5 atoms make the total charge on the −NO2 group almost zero. These findings of this calculation indicate that a tendency of electron transfer from N3 atoms to O2 atoms results in the five sensitizers producing NO2 gas when heated. The dipole moment μ of a compound is an important reference that reflects the molecule symmetry and the atomic charge distribution. By analyzing the dipole moments listed in Table 2, it is seen that the computational μ values of NPN, IPN, and EHN obtained at the two levels are rather close in magnitude. These results suggest that the thermal stability of the three alkyl nitrates is similar when they are in solvent. The very small value of TEGDN′s dipole moment μ indicates that its centers of positive and negative charge are very close and that its polarity is the least. 2.3 Prediction of the chemical reactivity The Mulliken populations of the selected bond analysis are shown in Table 3. As a whole, the larger the Mulliken populations, the more are the bonding overlaps. Therefore, bonds with large populations are relatively strong and resistant to rupture[31,32]. Although the Mulliken populations of C1−O2,
Key atomic charge and the dipole moments of the five sensitizers
C1 -0.05602 -0.13250 −0.05170 −0.12636 0.12784 0.06590 −0.04784 −0.12388 −0.06548 −0.14087
O2 -0.44755 -0.39849 −0.44468 −0.39609 −0.45678 −0.40447 −0.44565 −0.39760 −0.45134 −0.40310
N3 0.93291 0.73796 0.93606 0.74122 0.93768 0.74250 0.93363 0.73832 0.93669 0.74191
q/e O4 -0.42362 -0.33119 −0.42809 −0.33551 −0.42703 −0.33539 −0.42623 −0.33255 −0.42408 −0.32922
O5 -0.47907 -0.37417 −0.47433 −0.37170 −0.48047 −0.37745 −0.47836 −0.37284 −0.46800 −0.36337
H 0.22629 0.23838 0.21637 0.22905 0.23566 0.24856 0.22484 0.24076 0.22403 0.23674
Atomic charges q and dipole moments μ are obtained from the Mulliken population analysis.
C6 -0.67483 -0.71332 −0.45591 −0.48343 −0.65513 −0.69614 −0.26880 −0.28387 −0.04471 −0.11481
1030μ/(C·m) 13.3315 10.8718 14.3052 11.9496 14.0210 11.6290 13.8042 11.2881 3.2539 2.3042
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Table 3
The Mulliken populations of key bonds, the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE) at the HF/6-31G* and B3LYP /6-31G* levels (energies in a.u.) Mulliken population
Compound
Method HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G*
EN NPN IPN EHN TEGDN
C1−O2
O2−N3
N3−O4
N3−O5
C1−C6
0.1308 0.1745 0.1298 0.1568 0.1124 0.1491 0.1225 0.1587 0.1193 0.1462
0.2306 0.1557 0.2317 0.1523 0.2318 0.1532 0.2313 0.1556 0.2290 0.1515
0.4205 0.3625 0.4240 0.3657 0.4234 0.3626 0.4213 0.3625 0.4242 0.3672
0.3693 0.3081 0.3719 0.3085 0.3674 0.3055 0.3687 0.3076 0.3741 0.3101
0.3346 0.3635 0.3428 0.3648 0.3581 0.3730 0.3554 0.3507 0.3624 0.3560
O2−N3, N3−O4, N3−O5, and C1−C6 in the five acyclic nitrates differ slightly, they are consistent with the strength of the corresponding bonds in the title compounds. Obviously, the C1−O2 and O2−N3 have smaller Mulliken populations than the N3−O4, N3−O5, and C1−C6 type bonds do, indicating that the C1−O2 and O2−N3 bonds are weak; it can be predicted that the rupture of the C1−O2 or O2−N3 bond is an initiator during the thermolysis process. The results obtained from the Mulliken population analysis are found to almost coincide with the results of the bond length analysis mentioned previously. Moreover, it must be noted that these conclusions agree with those of Urbanski et al[48]. The chemical reactivity of molecules is affected by several factors. For example, the rate of a reaction can be accelerated by the Coulombic attraction between two reactants. In reactions of a nucleophile with an electrophile, the interaction between the HOMO (highest occupied molecular orbital) of the nucleophile with the LUMO (lowest unoccupied molecular orbital) of the electrophile contributes to the attraction between the two reactants. Studying HOMO and LUMO is expected to indicate whether the reaction is feasible and determine the relatively thermal stability of an individual molecule in the gas phase. The higher value of the energy gap (ΔE) resulting from the higher energy of LUMO and the lower energy of HOMO indicates that neither loss nor gain of electron will take place easily on the title compound and hence it has favorable thermal stability. Based on the data of the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE) shown in Table 3, the relative thermal stabilities of the five sensitizTable 4
Frontier orbital energy C6−C7 C6−O7
0.3444 0.3799 0.2045 0.2317
C6−C9 O7−C8
0.3022 0.3255 0.1873 0.2184
C9−C10 C9−O10
0.3420 0.3728 0.1945 0.2230
EHOMO
ELUMO
ΔE
−0.4748 −0.3134 −0.4724 −0.3105 −0.4710 −0.3091 −0.4464 −0.3058 −0.4405 −0.2718
0.1281 −0.0642 0.1308 −0.0614 0.1310 −0.0612 0.1300 −0.0630 0.1242 −0.0685
0.6029 0.3072 0.6032 0.2491 0.6020 0.2479 0.5764 0.3028 0.5647 0.2033
ers in the gas phase are to some degree assigned as follows: (the least stable) TEGDN
The calculated total energy (E0), the zero-point energy (ZPE), the values of thermal correction (HT), and the heats of formation (HOFs) of the reference compounds
Compound C2H6 CH3ONO2 CH4 C2H5OH H2O (CH2OH)2
E0 −79.755176 −320.134683 −40.473161 −154.953491 −76.387803 −230.150659
B3LYP/6-31G* ZPE 197.55 143.77 118.73 210.85 55.53 223.32
HT 11.73 15.75 10.02 13.92 9.92 17.05
E0 −79.148995 −318.413301 −40.147395 −153.989724 −75.987768 −228.830472
HF/6-31G* ZPE 209.41 158.22 125.44 225.85 60.33 241.42
HT 11.79 15.36 9.98 13.95 9.92 16.86
HOF[38,45,46] −83.80 −123.00 −74.40 −235.31 −241.827 − 4 4 4 . 93
E0 is in a.u.; ZPE, HOFs, and HT are in kJ·mol−1; the scaling factors for the ZPE are 0.96 and 0.89 at the DFT and HF levels, respectively.
Xiulin Zeng et al. / Acta Physico-Chimica Sinica, 2007, 23(2): 192-197
Table 5
The calculated total energy (E0), the zero-point energy (ZPE), the values of thermal correction (HT), and the heats of formation (HOFs) of the title compounds
Compound
E0 −359.425021 −398.715691 −398.710417 −595.141165 −1100.396872
EN IPN NPN EHN TEGDN
B3LYP/6-31G* ZPE HT 218.89 19.04 292.42 22.84 294.03 23.00 669.35 52.51 724.56 87.55
HOF −155.972 −190.896 −175.279 −272.376 −790.733
E0 −357.422334 −396.432230 −396.427868 −591.451449 −1094.239015
HF/6-31G* ZPE 237.93 315.94 317.88 718.35 788.66
HT 18.74 22.53 22.68 48.02 81.10
HOF −154.205 −188.967 −168.424 −264.422 −802.436
E0 is in a.u.; ZPE, HOF, and HT are in kJ·mol–1; the scaling factors for the ZPE are 0.96 and 0.89 at the DFT and HF levels, respectively.
expected to yield fair to good results, despite the fact that it does not include a complete treatment of electron correlation because errors are canceled by the use of isodesmic reactions. The density functional methods, although not truly ab initio, include electron correlation with only a moderate increase in the computing cost, as compared to HF, by using the functional of the electron density. By analyzing the results of the HOFs from Table 5, it is seen that the values obtained at the HF and B3LYP levels are rather close in magnitude, whereas HOFs obtained from the B3LYP/6-31G* level agree rather well with the available experimental values. Thus, if the HOFs from DFT are referred to as the criteria, the recommended HOF values for EN, IPN, NPN, EHN, and TEGDN, including our precision, judgment of methodology, and accuracy are −155.972, −190.896, −175.279, −272.376, and −790.733 kJ·mol−1, respectively.
3 Conclusions This study has yielded a wealth of quantum chemical information on the molecular geometries, the electronic structure, and the frontier orbital energies of ethyl nitrate (EN), n-propyl nitrate (NPN), isopropyl nitrate (IPN), 2-ethylhexyl nitrate (EHN), and tetraethylene glycol dinitrate (TEGDN). It is important to elucidate the relationship between the molecular structure of the sensitizers and their chemical properties. The geometries of the five title compounds obtained at the B3LYP level are slightly better than those obtained at the HF level, when compared with the experimental geometrical parameters. On the basis of the Mulliken populations and the bond lengths, the dissociation of the O2−N3 for acyclic nitrates in the gas phase is reasonably acceptable. The charge distribution analysis indicates a tendency of electron transfer from N3 atoms to O2 atoms; consequently, the five sensitizers produce NO2 gas during the dissociation of the O2−N3 weak bond. Finally, from the data of the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE), the relative thermal stability ordering of the five sensitizers is estimated. The DFT and ab initio theories were also used for the prediction of HOFs of the title compounds. When compared with the available experimental values, the very good agreement obtained for the B3LYP/6-31G* level and the relatively good agreement for the HF/6-31G* level confirm that the HOFs
from DFT with the isodesmic reaction can be referred to as the criteria for the five sensitizers. Hence, the recommended HOF values for EN, IPN, NPN, EHN, and TEGDN are −155.972, −190.896, −175.279, −272.376, and −790.733 kJ·mol−1, respectively. This study provides accurate HOFs of the five sensitizers for researchers investigating explosives to calculate the explosive detonation parameters. Furthermore, from the aspects of chemical kinetics and thermodynamics, an investigation on the thermolysis behavior of the five sensitizers is in progress, using theoretical calculation and the experimental procedure.
Acknowledgments: The authors thank Prof. JU Xue-Hai, School of Chemical Engineering, Nanjing University of Science & Technology, for acting as an advisor for this research.
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ARTICLE
Molecular Structure, Electronic Structure and Heats of Formation of Explosive Sensitizers Xiulin Zeng*,
Wanghua Chen,
Jiacong Liu
School of Chemical Engineering, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Abstract:
Quantum chemical calculations at the HF/6-31G* and B3LYP/6-31G* levels have been carried out on five explosive
sensitizers: ethyl nitrate (EN), n-propyl nitrate (NPN), isopropyl nitrate (IPN), 2-ethylhexyl nitrate (EHN), and tetraethylene glycol dinitrate (TEGDN). Theoretical studies have yielded a wealth of quantum chemical information on the molecular geometries, electronic structures, and energies of the title compounds. On the basis of the Mulliken populations and bond lengths, the O2−N3 fission is acceptable. Charge distribution analysis indicates that the five nitrates produce NO2 gas during the dissociation of the O2−N3 weak bond. The relative thermal stability ordering of the five nitrates was estimated on the basis of the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE). The heats of formation (HOFs) of the five sensitizers, EN, IPN, NPN, EHN, and TEGDN, were calculated from the isodesmic reactions and were −155.972, −190.896, −175.279, −272.376, and −790.733 kJ·mol–1, respectively. Key Words:
Explosive sensitizers; Mulliken population; Frontier orbital energy; Heat of formation (HOF); Isodesmic reaction
The major challenge in the design and application of explosives is the achievement of the right oxygen and fuel mixture to ensure the development of high overpressure and high temperature. In military explosives, some sensitizers are commonly added to the mixture, making it more easy for the mixture to be ignited and to grow to detonation from hot spots such as those caused by sparks, flame, and other sources of heat and high temperature. These sensitizers are relatively unstable molecules, and their decomposition at low temperatures produces free radicals[1−7]. Heat of formation (HOF) is the key property that is used to assess the potential performance of an energetic material in a gun or warhead. Also, HOF is an importance aspect of research in thermochemistry and is directly related to the output properties of an explosive. Using the HOFs of detonation products and explosives, detonation parameters such as heat of detonation, temperature of detonation, detonation velocity, and CJ pressure of detonation[8−14] can be predicted. The sensitizers investigated in this study are ethyl nitrate (EN), n-propyl nitrate (NPN), isopropyl nitrate (IPN), 2-ethylhexyl nitrate (EHN), and tetraethylene glycol dinitrate (TEGDN).
Organic nitrates have been known since the early 1900s. The chemistry of organic nitrates has been a significant area of research since 1930s. Comprehensive reviews are available on their use as additives to explosives and propellants. Since then, organic nitrates have been extensively investigated for their potential use as reactive species in other areas of science and technology. Organic nitrates have also been used to improve ignition in automotive fuels[15−27]. The five acyclic nitrates investigated in this study are used as explosive sensitizers because they possess a weak O−N bond, which is the site of thermal and chemical reactivity. Despite the growing interest in the development of explosives, relatively few quantum chemical computations on explosive sensitizers have been reported so far. Geometrical information is important for understanding the molecular properties of sensitizers that contribute to the sensitizing mechanism; therefore, theoretical calculations have been performed using ab initio and density functional methods. There are several methods that can be used to predict the heats of formation of gas phases from quantum mechanical calculations. Although HOFs were not calculated directly using the
Received: June 21, 2006; Revised: September 14, 2006. * Corresponding author. Email: [email protected]; Tel: +8625-84315526-808. Copyright © 2007, Chinese Chemical Society and College of Chemistry and Molecular Engineering, Peking University. Published by Elsevier BV. All rights reserved. Chinese edition available online at www.whxb.pku.edu.cn
Xiulin Zeng et al. / Acta Physico-Chimica Sinica, 2007, 23(2): 192-197
ab initio MO method and the density functional theory (DFT) method, the results of the geometries and the energies obtained using the two methods are quite reliable. Therefore, the isodesmic reaction has to be designed to derive the HOFs from the calculated total energies and the vibrational analysis results[28−38]. In this study, theoretical calculations were carried out on five explosive sensitizers at the HF[39] and B3LYP[40,41] levels, using the 6-31G* basis set[42]. The molecular geometries, the electronic structure, and the frontier orbital energy were obtained and the HOFs were evaluated.
ΔnRT for the reactions of an ideal gas. For the isodesmic reactions (1a) and (1b), Δn=0, and hence Δ(pV)=0. Computations have been carried out using the Gaussian 98 package[47] at the B3LYP and HF levels on a Pentium personal computer in Safety Engineering and Technology Laboratory. The optimizations were carried out without any symmetry restrictions using the default convergence criteria in the programs. All the optimized structures were characterized as true local energy minima on the potential energy surfaces without imaginary frequencies.
1
2
Computational methodology
The full geometry optimizations of the five sensitizers, EN, NPN, IPN, EHN, and TEGDN, were carried out using Becke′s three-parameter hybrid method and the exchange functional of Yee, Yang, and Parr[40], with the 6-31G* basis set. These computations were also done at the HF level with the 6-31G* basis set. The molecular structure and other parameters were obtained. Isodesmic reactions were designed to predict the HOFs of the five title compounds. Errors in the absolute quantities from quantum chemical calculations are often systematic. To compensate for some of the systematic errors, isodesmic reactions, which conserve the number of each type of bond in the reactants and products, are used to obtain more accurate heats of formation. The so-called isodesmic reaction processes, in which the number of each kind of formal bond is conserved, are used with the application of the bond separation reaction (BSR) criteria[43,44]. The HOFs of the five sensitizers at 298 K were calculated from the following isodesmic reactions: CnH2n+1ONO2+(n−1)CH4→(n−1)C2H6+CH3ONO2 (1a) O2NO(CH2CH2O)4NO2+2CH4+3H2O→ 2HOCH2CH2OH+2CH3CH2OH+2CH3ONO2 (1b) where n is the number of carbon atoms in the title compound. Eq.(1a) is treated as an isodesmic reaction for EN, IPN, NPN, or EHN, and Eq.(1b) is treated as an isodesmic reaction for TEGDN. For reactions (1a) and (1b), the heat of the reaction ΔH298 at 298 K can be calculated from the following equation: ΔH298=ΣΔHf,P−ΣΔHf,R (2) where ΔHf,R and ΔHf,P are the HOFs of the reactants and products at 298 K, respectively. Both the experimental HOFs of the reference compounds CH4, C2H6, CH3ONO2, H2O, C2H5OH, and HOCH2CH2OH are available from Refs.[45,46]. The HOFs of the five title compounds can be determined when the heat of the reaction ΔH298 is known. ΔH298 can be calculated using the following expression: ΔH298=ΔE298+Δ(pV)=ΔE0+ΔZPE+ΔHT+ΔnRT (3) where ΔE0 is the change in the total energy between the products and the reactants at 0 K, ΔZPE is the difference between the zero-point energies (ZPE) of the products and the reactants at 0 K, and ΔHT is the thermal correction from 0 K to 298 K. The Δ(pV) value in Eq.(3) is the pV work term; it is equal to
Results and discussion
2.1 Molecular structure The optimized geometries of the five acyclic nitrates and the atom numbering are shown in Fig.1. The geometrical parameters are first discussed. There is a noticeable feature in the optimized geometry of TEGDN. The following discussion only deals with its half moiety because of the completely symmetrical geometry of TEGDN. The selected bond lengths, the bond angles, and the dihedral angles at the HF/6-31G* and B3LYP/6-31G* levels for the title compounds are shown in Table 1. As seen from Table 1, the calculated structural parameters at the HF/6-31G* level are consistent with those at the B3LYP/6-31G* level. For the bond length of C1−O2, O2−N3, N3−O4, N3−O5, and C1−C6, the HF values are shorter compared with B3LYP results, and for the bond angle of C1−O2−N3, O2−N3−O4, and O2−N3−O5, the HF values are larger than the B3LYP results. In addition, when compared with the experimental geometrical parameters[48−51], the results obtained at the B3LYP level are more favorable than those obtained at the HF level because the former method fully takes into consideration the effects of electron correlation and repulsion.
Fig.1
The structures and atom numbering of the five sensitizers
Xiulin Zeng et al. / Acta Physico-Chimica Sinica, 2007, 23(2): 192-197
Table 1 Compound EN
NPN IPN EHN TEGDN
The selected geometrical parameters of the five sensitizers at the HF/6-31G* and B3LYP /6-31G* levels
Method HF/6-31G* B3LYP/6-31G* Exp. HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G*
C1−O2 0.1441 0.1452 0.1443 0.1438 0.1449 0.1454 0.1466 0.1442 0.1452 0.1433 0.1443
Bond length (nm) O2−N3 N3−O4 N3−O5 0.1329 0.1177 0.1188 0.1415 0.1207 0.1216 0.1405 0.1204 0.1209 0.1328 0.1178 0.1187 0.1412 0.1208 0.1216 0.1328 0.1178 0.1188 0.1410 0.1208 0.1217 0.1329 0.1178 0.1188 0.1416 0.1207 0.1215 0.1330 0.1177 0.1186 0.1416 0.1206 0.1214
C1−C6 0.1515 0.1520 0.1519 0.1517 0.1523 0.1518 0.1524 0.1527 0.1533 0.1516 0.1524
C1O2N3 117.4 114.6 113.0 116.4 114.1 118.0 115.6 117.4 114.7 116.3 113.8
Bond angle and dihedral angle (degree) O2N3O4 O2N3O5 C1O2N3O4 C1O2N3O5 114.2 118.4 −177.8 2.5 2.9 112.5 118.0 −177.5 112.2 118.2 0.0 114.0 118.1 −180.0 0.0 112.8 117.6 −180.0 −2.9 113.8 118.6 177.5 −2.5 112.6 118.3 178.0 3.1 113.8 118.5 −177.3 3.3 112.5 118.1 −177.2 0.0 113.9 117.9 −180.0 0.0 112.6 117.4 −180.0
See Fig.1 for atom numbering; experimental results of EN from Ref.[48−51].
Previous experimental and theoretical studies[25−27,48] have shown that the CO−NO2 group in nitric esters normally has a planar framework. From Fig.1 and Table 1, it can be seen that the C−O−NO2 of the two linear nitrates, NPN and TEGDN, are completely coplanar. The C−O−NO2 of the two-branched nitrates, IPN, EHN, and EN, are essentially planar. These results imply that rotation around the O−N in the nitrates is hardly possible. However, it should be mentioned that there is a noticeable variation in the values of the C1−O2 and O2−N3 bond lengths compared with the other parameters, implying that these geometrical parameters are more sensitive to different molecular structures. Moreover, by comparing the bond lengths among O2−N3, N3−O4, and N3−O5, it was found that the bond length of O2−N3 was obviously larger than that of the other two. It is well known that the shorter the bond length, the stronger the strength of the bond and vice versa. Hence, it can be concluded that the dissociation of the O2−N3 bond is the most probable pathway for acyclic nitrates in the gas phase. 2.2 Electronic structure Table 2 shows the selected atomic charge distributions and the dipole moments μ of the five sensitizers obtained at the HF/6-31G* and B3LYP/6-31G* levels. The charge on the α-C(C1) atoms obtained using the two methods are all negative and very similar in value in EN, NPN, EHN, and TEGDN, but the charge on the α-C(C1) atom in IPN was positive because of Table 2 Compound EN NPN IPN EHN TEGDN
Method HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G*
−CH3 substitution to the α-carbon. This is an expected result because the α-C(C1) atoms of EN, NPN, EHN, and TEGDN are secondary C atoms and that of IPN is a tertiary C atom. It is interesting to note that the atomic charge in the O−NO2 groups is almost identical in the case of the five title compounds. The relatively higher positive charge on the N3 atoms and the negative charge on the O4 and O5 atoms make the total charge on the −NO2 group almost zero. These findings of this calculation indicate that a tendency of electron transfer from N3 atoms to O2 atoms results in the five sensitizers producing NO2 gas when heated. The dipole moment μ of a compound is an important reference that reflects the molecule symmetry and the atomic charge distribution. By analyzing the dipole moments listed in Table 2, it is seen that the computational μ values of NPN, IPN, and EHN obtained at the two levels are rather close in magnitude. These results suggest that the thermal stability of the three alkyl nitrates is similar when they are in solvent. The very small value of TEGDN′s dipole moment μ indicates that its centers of positive and negative charge are very close and that its polarity is the least. 2.3 Prediction of the chemical reactivity The Mulliken populations of the selected bond analysis are shown in Table 3. As a whole, the larger the Mulliken populations, the more are the bonding overlaps. Therefore, bonds with large populations are relatively strong and resistant to rupture[31,32]. Although the Mulliken populations of C1−O2,
Key atomic charge and the dipole moments of the five sensitizers
C1 -0.05602 -0.13250 −0.05170 −0.12636 0.12784 0.06590 −0.04784 −0.12388 −0.06548 −0.14087
O2 -0.44755 -0.39849 −0.44468 −0.39609 −0.45678 −0.40447 −0.44565 −0.39760 −0.45134 −0.40310
N3 0.93291 0.73796 0.93606 0.74122 0.93768 0.74250 0.93363 0.73832 0.93669 0.74191
q/e O4 -0.42362 -0.33119 −0.42809 −0.33551 −0.42703 −0.33539 −0.42623 −0.33255 −0.42408 −0.32922
O5 -0.47907 -0.37417 −0.47433 −0.37170 −0.48047 −0.37745 −0.47836 −0.37284 −0.46800 −0.36337
H 0.22629 0.23838 0.21637 0.22905 0.23566 0.24856 0.22484 0.24076 0.22403 0.23674
Atomic charges q and dipole moments μ are obtained from the Mulliken population analysis.
C6 -0.67483 -0.71332 −0.45591 −0.48343 −0.65513 −0.69614 −0.26880 −0.28387 −0.04471 −0.11481
1030μ/(C·m) 13.3315 10.8718 14.3052 11.9496 14.0210 11.6290 13.8042 11.2881 3.2539 2.3042
Xiulin Zeng et al. / Acta Physico-Chimica Sinica, 2007, 23(2): 192-197
Table 3
The Mulliken populations of key bonds, the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE) at the HF/6-31G* and B3LYP /6-31G* levels (energies in a.u.) Mulliken population
Compound
Method HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G* HF/6-31G* B3LYP/6-31G*
EN NPN IPN EHN TEGDN
C1−O2
O2−N3
N3−O4
N3−O5
C1−C6
0.1308 0.1745 0.1298 0.1568 0.1124 0.1491 0.1225 0.1587 0.1193 0.1462
0.2306 0.1557 0.2317 0.1523 0.2318 0.1532 0.2313 0.1556 0.2290 0.1515
0.4205 0.3625 0.4240 0.3657 0.4234 0.3626 0.4213 0.3625 0.4242 0.3672
0.3693 0.3081 0.3719 0.3085 0.3674 0.3055 0.3687 0.3076 0.3741 0.3101
0.3346 0.3635 0.3428 0.3648 0.3581 0.3730 0.3554 0.3507 0.3624 0.3560
O2−N3, N3−O4, N3−O5, and C1−C6 in the five acyclic nitrates differ slightly, they are consistent with the strength of the corresponding bonds in the title compounds. Obviously, the C1−O2 and O2−N3 have smaller Mulliken populations than the N3−O4, N3−O5, and C1−C6 type bonds do, indicating that the C1−O2 and O2−N3 bonds are weak; it can be predicted that the rupture of the C1−O2 or O2−N3 bond is an initiator during the thermolysis process. The results obtained from the Mulliken population analysis are found to almost coincide with the results of the bond length analysis mentioned previously. Moreover, it must be noted that these conclusions agree with those of Urbanski et al[48]. The chemical reactivity of molecules is affected by several factors. For example, the rate of a reaction can be accelerated by the Coulombic attraction between two reactants. In reactions of a nucleophile with an electrophile, the interaction between the HOMO (highest occupied molecular orbital) of the nucleophile with the LUMO (lowest unoccupied molecular orbital) of the electrophile contributes to the attraction between the two reactants. Studying HOMO and LUMO is expected to indicate whether the reaction is feasible and determine the relatively thermal stability of an individual molecule in the gas phase. The higher value of the energy gap (ΔE) resulting from the higher energy of LUMO and the lower energy of HOMO indicates that neither loss nor gain of electron will take place easily on the title compound and hence it has favorable thermal stability. Based on the data of the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE) shown in Table 3, the relative thermal stabilities of the five sensitizTable 4
Frontier orbital energy C6−C7 C6−O7
0.3444 0.3799 0.2045 0.2317
C6−C9 O7−C8
0.3022 0.3255 0.1873 0.2184
C9−C10 C9−O10
0.3420 0.3728 0.1945 0.2230
EHOMO
ELUMO
ΔE
−0.4748 −0.3134 −0.4724 −0.3105 −0.4710 −0.3091 −0.4464 −0.3058 −0.4405 −0.2718
0.1281 −0.0642 0.1308 −0.0614 0.1310 −0.0612 0.1300 −0.0630 0.1242 −0.0685
0.6029 0.3072 0.6032 0.2491 0.6020 0.2479 0.5764 0.3028 0.5647 0.2033
ers in the gas phase are to some degree assigned as follows: (the least stable) TEGDN
The calculated total energy (E0), the zero-point energy (ZPE), the values of thermal correction (HT), and the heats of formation (HOFs) of the reference compounds
Compound C2H6 CH3ONO2 CH4 C2H5OH H2O (CH2OH)2
E0 −79.755176 −320.134683 −40.473161 −154.953491 −76.387803 −230.150659
B3LYP/6-31G* ZPE 197.55 143.77 118.73 210.85 55.53 223.32
HT 11.73 15.75 10.02 13.92 9.92 17.05
E0 −79.148995 −318.413301 −40.147395 −153.989724 −75.987768 −228.830472
HF/6-31G* ZPE 209.41 158.22 125.44 225.85 60.33 241.42
HT 11.79 15.36 9.98 13.95 9.92 16.86
HOF[38,45,46] −83.80 −123.00 −74.40 −235.31 −241.827 − 4 4 4 . 93
E0 is in a.u.; ZPE, HOFs, and HT are in kJ·mol−1; the scaling factors for the ZPE are 0.96 and 0.89 at the DFT and HF levels, respectively.
Xiulin Zeng et al. / Acta Physico-Chimica Sinica, 2007, 23(2): 192-197
Table 5
The calculated total energy (E0), the zero-point energy (ZPE), the values of thermal correction (HT), and the heats of formation (HOFs) of the title compounds
Compound
E0 −359.425021 −398.715691 −398.710417 −595.141165 −1100.396872
EN IPN NPN EHN TEGDN
B3LYP/6-31G* ZPE HT 218.89 19.04 292.42 22.84 294.03 23.00 669.35 52.51 724.56 87.55
HOF −155.972 −190.896 −175.279 −272.376 −790.733
E0 −357.422334 −396.432230 −396.427868 −591.451449 −1094.239015
HF/6-31G* ZPE 237.93 315.94 317.88 718.35 788.66
HT 18.74 22.53 22.68 48.02 81.10
HOF −154.205 −188.967 −168.424 −264.422 −802.436
E0 is in a.u.; ZPE, HOF, and HT are in kJ·mol–1; the scaling factors for the ZPE are 0.96 and 0.89 at the DFT and HF levels, respectively.
expected to yield fair to good results, despite the fact that it does not include a complete treatment of electron correlation because errors are canceled by the use of isodesmic reactions. The density functional methods, although not truly ab initio, include electron correlation with only a moderate increase in the computing cost, as compared to HF, by using the functional of the electron density. By analyzing the results of the HOFs from Table 5, it is seen that the values obtained at the HF and B3LYP levels are rather close in magnitude, whereas HOFs obtained from the B3LYP/6-31G* level agree rather well with the available experimental values. Thus, if the HOFs from DFT are referred to as the criteria, the recommended HOF values for EN, IPN, NPN, EHN, and TEGDN, including our precision, judgment of methodology, and accuracy are −155.972, −190.896, −175.279, −272.376, and −790.733 kJ·mol−1, respectively.
3 Conclusions This study has yielded a wealth of quantum chemical information on the molecular geometries, the electronic structure, and the frontier orbital energies of ethyl nitrate (EN), n-propyl nitrate (NPN), isopropyl nitrate (IPN), 2-ethylhexyl nitrate (EHN), and tetraethylene glycol dinitrate (TEGDN). It is important to elucidate the relationship between the molecular structure of the sensitizers and their chemical properties. The geometries of the five title compounds obtained at the B3LYP level are slightly better than those obtained at the HF level, when compared with the experimental geometrical parameters. On the basis of the Mulliken populations and the bond lengths, the dissociation of the O2−N3 for acyclic nitrates in the gas phase is reasonably acceptable. The charge distribution analysis indicates a tendency of electron transfer from N3 atoms to O2 atoms; consequently, the five sensitizers produce NO2 gas during the dissociation of the O2−N3 weak bond. Finally, from the data of the frontier orbital energy (EHOMO, ELUMO) and the energy gap (ΔE), the relative thermal stability ordering of the five sensitizers is estimated. The DFT and ab initio theories were also used for the prediction of HOFs of the title compounds. When compared with the available experimental values, the very good agreement obtained for the B3LYP/6-31G* level and the relatively good agreement for the HF/6-31G* level confirm that the HOFs
from DFT with the isodesmic reaction can be referred to as the criteria for the five sensitizers. Hence, the recommended HOF values for EN, IPN, NPN, EHN, and TEGDN are −155.972, −190.896, −175.279, −272.376, and −790.733 kJ·mol−1, respectively. This study provides accurate HOFs of the five sensitizers for researchers investigating explosives to calculate the explosive detonation parameters. Furthermore, from the aspects of chemical kinetics and thermodynamics, an investigation on the thermolysis behavior of the five sensitizers is in progress, using theoretical calculation and the experimental procedure.
Acknowledgments: The authors thank Prof. JU Xue-Hai, School of Chemical Engineering, Nanjing University of Science & Technology, for acting as an advisor for this research.
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